A ball in flight is modeled by the function
h(t)=-16t²+128t. Find the maximum height and time to get there.

Question

A ball in flight is modeled by the function 
h(t)=-16t²+128t. Find the maximum height and time to get there.

mertsj · Answer

The maximum height will be the y coordinate of the vertex.  Can you find that?

anonymous · Answer

huh?

mertsj · Answer

Do you know that the graph of that function is a parabola?

anonymous · Answer

yes

mertsj · Answer

So then you know that it has either a high point or a low point?

anonymous · Answer

yes

mertsj · Answer

which one does this problem have...a high point (maximum) or a low point (minimum)?

anonymous · Answer

maximum

mertsj · Answer

It has a hight point (maximum) because the coefficient of the t^2 term is negative.

mertsj · Answer

Do you know that the high point is called the vertex?

anonymous · Answer

yes

mertsj · Answer

Do you know that the vertex is represented by an ordered pair that has an x value and a y value?

anonymous · Answer

yes

mertsj · Answer

Ok.  we need to find that highest point (vertex).  The x coordinate of the vertex is x=-b/2a
Calculate that.

mertsj · Answer

$$x=\frac{-128}{2(-16)}=\frac{-128}{-32} = 4$$

mertsj · Answer

$$y=-16(4)^2+128(4)= 256$$

mertsj · Answer

So the vertex is (4,256) and the maximum height of the ball is 256 feet.

mertsj · Answer

And that happens when the time is 4 seconds.